A Fast and Stable Solver for Singular Integral Equations on Piecewise Smooth Curves

A scheme is presented for the numerical solution of singular integral equations on piecewise smooth curves. It relies on several techniques: reduction, Nystr¨om discretization, composite quadrature, recursive compressed inverse preconditioning, and multipole acceleration. The scheme is fast and stable. Its computational cost grows roughly logarithmically with the precision sought and linearly with overall system size. When the integral equation models a boundary value problem, the achievable accuracy may be close to the condition number of that problem times machine epsilon. This is illustrated by application to elastostatic problems involving zigzag-shaped cracks with up to twenty thousand corners and branched cracks with hundreds of triple-junctions. Key words. singular integral equation, elasticity, corner singularity, multi-wedge points AMS subject classifications. 45E05, 65R20, 74B05

• Type: Journal
• Year: 2011
• Where: SIAMSC
• Authors: Johan Helsing
• Keywords: Integral Equation, Integral Equation Models, SIAMSC 2011, Singular Integral Equation